(rectangular section): [ \phi M_n \geq M_u ] [ M_n = A_ps f_ps \left(d_p - \fraca2\right) ] Where (f_ps) is stress in prestressing steel at ultimate (not (f_py) or (f_pu)) – determined by strain compatibility or approximate ACI equation: [ f_ps = f_pu \left(1 - \frac\gamma_p\beta_1 \cdot \frac\rho_p f_puf'_c\right) ] 5. Shear Design in Prestressed Concrete Prestress improves shear capacity by reducing principal tension. Nilson details the ACI method :
: Service stress bottom = P_e/A – P_e·e/S_b + M_ser/S_b = compression OK (all ≤ 0.45f'_c). Top fiber may see small tension (< 3.16 MPa). Diseno De Estructuras De Concreto Presforzado Nilson Pdf
Introduction Since its emergence in the early 20th century, prestressed concrete has revolutionized the construction of bridges, building floors, water tanks, and foundations. Arthur H. Nilson’s Design of Prestressed Concrete Structures remains a cornerstone reference for engineers worldwide. This article synthesizes the core concepts, design philosophies, and calculation methods presented in Nilson’s work, focusing on the two principal systems: pretensioning and post-tensioning . 1. Fundamental Concepts of Prestressing Prestressing introduces permanent internal stresses to counteract tensile forces from service loads. Unlike reinforced concrete, where steel begins working only after cracking, prestressed concrete remains primarily in compression. Basic Principle Concrete is strong in compression but weak in tension (approximately 10% of compressive strength). By applying a compressive force (P/A) and a bending moment (P·e/I), tensile stresses from loads are neutralized. The net stress at any fiber is: (rectangular section): [ \phi M_n \geq M_u ]
[ f = -\fracPA \pm \fracP \cdot e \cdot yI \pm \fracM \cdot yI ] Top fiber may see small tension (< 3
: Elastic shortening (40 MPa), creep (50 MPa), shrinkage (30 MPa), relaxation (20 MPa) → total 140 MPa → effective stress = 1395 – 140 = 1255 MPa → P_e = 1255×1680 = 2108 kN.
(service moment = 360 kN·m, allowable tension = 0.5√40 = 3.16 MPa). S_required = M / f_t = 360e6 / 3.16 = 114e6 mm³ → Choose I-section (top flange 200×60, web 150×400, bottom flange 300×80).